Master's Dissertation
DOI
10.11606/D.55.2011.tde-12052011-105031
Document
Author
Full name
Vinicius Casteluber Laass
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2011
Supervisor
Committee
Manzoli Neto, Oziride (President)
Borsari, Lucilia Daruiz
Tengan, Eduardo
Title in Portuguese
Grupos de tranças do espaço projetivo
Keywords in Portuguese
Apresentação de grupos
Espaço projetivo
Espaços de configuração
Grupos de tranças
Abstract in Portuguese
Dada uma superfície M, definiremos os grupos de tranças de M, denotado por 'B IND. n' (M), geometricamente e usando a noção de espaços de confiuração. Mostraremos a equivalência das definições. Na mesma linha de raciocínio, definiremos os grupos de tranças puras de superfícies 'P IND. n' (M). Apresentaremos as propriedades mais importantes dos grupos de tranças do plano e mostraremos que 'B IND. n' ('R POT. 2') injeta em 'B IND. n' (M), para muitas superfícies M. Mais detalhadamente, obteremos a apresentação de 'B IND. n' ('RP POT. 2' ) e 'P IND. n'('RP POT. 2')
Title in English
Braid groups of projective plane
Keywords in English
Braid groups
Configuration spaces
Presentation of groups
Projective plane
Abstract in English
For a surface M, we define the braid groups of M, 'B IND. n'(M), geometricaly and using the notion of configuration spaces. We show the equivalence of these definitions. In the sequence, we define the pure braid group of M, 'P IND. n' (M). We present the most important properties of braid groups of the plane and we show that 'B IND. n''('R POT. 2') embedds in 'B IND. n' (M), for almost all M. In a more detailed fashion, we present 'B IND. n' ('RP POT. 2') and 'P IND. n' ('RP POT. 2)

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Publishing Date
2011-05-12

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